Kenneth S. answered • 06/22/17
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The question submitted includes: Explain how did you applied these?
I would correct that sentence as follows: Explain how did you applied these?
To obtain the square root of a number (other than that of an already perfect square such as √121 = 11), the common method is to use a calculator. No longer taught is a boring and difficult method to do extraction of a square root by hand.
To take the square root of a large composite number, one learns to rewrite the number in its unique prime factorization.
Example: consider √6048. begin by obtaining 3(2016) = 3(3)(672) = 32•4•168 = 32•42•42=32•24•2•3•7
I would correct that sentence as follows: Explain how did you applied these?
To obtain the square root of a number (other than that of an already perfect square such as √121 = 11), the common method is to use a calculator. No longer taught is a boring and difficult method to do extraction of a square root by hand.
To take the square root of a large composite number, one learns to rewrite the number in its unique prime factorization.
Example: consider √6048. begin by obtaining 3(2016) = 3(3)(672) = 32•4•168 = 32•42•42=32•24•2•3•7
Note: numbers are divisible by 3 if the sum of their digits is a multiple of 3
Taking the square root of each factor gives √6048 = 3(22)√(2•3•7) = 12√42
Another method is based on common (base10) logarithms):
log 6048 = 3.781611782
half of that logarithm is 1.890805891
101.890805891 = = 77.76888838
check: √6048 = 77.76888838 (the latter work was done on a Casio fx-350ES Plus)
Taking the square root of each factor gives √6048 = 3(22)√(2•3•7) = 12√42
Another method is based on common (base10) logarithms):
log 6048 = 3.781611782
half of that logarithm is 1.890805891
101.890805891 = = 77.76888838
check: √6048 = 77.76888838 (the latter work was done on a Casio fx-350ES Plus)
Kenneth S.
Right, Katie! I copied & pasted, but failed to edit perfectly.
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06/22/17
Katie B.
06/22/17